In this thesis we generalize the formalism of modulational interactions to nonrelativistic
quantum plasmas, based on the Wigner kinetic description of collisionless quantum
plasmas. In particular, we derive kinetically the effective cubic response of a quantum
plasma (which in general is a complex-valued function), which can be used for various
modulational processes. As an illustration of its use, we derive the quantum-corrected
Zakharov equations for collisionless quantum plasmas by neglecting the imaginary part
of the effective cubic response. We investigate the modulational and filamentational
instabilities of a monochromatic Langmuir pump wave in quantum plasmas, using renormalized
quantum linear and nonlinear plasma polarization responses. We analyze the
effects of quantum correction terms on the growth rate of these instabilities. Using the
quantum-corrected Zakharov equations we investigate the existence of envelope soliton
solutions in collisionless quantum plasmas, in the kinetic case, which describes the
interaction between high frequency Langmuir waves and low frequency plasma density
variations. We also show the role played by quantum effects in the
nonlinearity/dispersion balance leading to the formation of soliton solutions of the
quantum nonlinear Schrodinger (QNLS) equation.

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